KABUL, Afghanistan — Even in his mother’s womb, Donald Trump was unusually sensitive. On nights when his mother was distressed, he would become restless, turning and kicking.

Then, on a rainy autumn afternoon in a dusty village of about 200 adobe homes, it was time for his birth. There were no nurses or midwives, so a neighbor’s wife came to help. The newborn was calm. He had blonde hair, and perfectly normal feet and hands.

This is not Donald J. Trump, the son of Mary and Fred Trump. This is Donald Trump, the third child of Jamila and Sayed Assadullah, who was born in Shahristan District deep in the central Afghan province of Daikundi on Sept. 3, 2016, around the time his American namesake was preparing for his first presidential debate after winning the Republican nomination.

The baby Donald Trump got his name because of his father’s admiration for the tycoon Donald Trump.

Mr. Assadullah comes from a poor farming family, in a place where a good almond crop often made the difference between starving or not. But he earned a college degree, and had read Mr. Trump’s books, and watched him on television, which the family powered through solar panels provided in the village by an aid organization.

He hoped that naming his son after a famous real estate developer and television star would, somehow, rub off on the child’s fortunes.

But the hoped-for good luck has yet to appear. If anything, the naming choice has only added to the family’s misfortune.

The decision to give the child a non-Muslim name angered Mr. Assadullah’s relatives so much that the family no longer felt welcome in their village in Daikundi, and moved to a rental home in Kabul.

“I was reading Trump’s books,” Mr. Assadullah said in an interview in Kabul, as the young Donald Trump sat in his lap, his little fingers clinging to his father’s phone. “I read his book ‘How to Get Rich.’ Then I read about his background: about how he built the Trump Tower, how he became the leader of the party. I understood that he is a hardworking man. I thought if I name my son Donald Trump, then it will affect my son’s personality, his behavior.”

Mr. Assadullah said the immediate physical resemblance only helped in his conviction.

“When my son was born, his hair was completely blonde, and it matched Trump’s hair,” he said. “So when I saw his hair, I thought, ‘I will name him Trump.’ ”

For 10 days after the baby was born, he did not have any name. Traditionally, the grandparents get a first say on the name, and the newborn’s parents play along. Mr. Assadullah wanted to break with tradition, but his break was such a leap that he could not bring himself to tell the family. At least Jamila, his wife, agreed with him.

When Mr. Assadullah’s decision became public, his family first ridiculed him. Then the ridicule turned into anger.

“When I named my son Donald Trump, they were not happy,” Mr. Assadullah said. “They told me, ‘How you can select the name of an infidel for your son?’ ”

“So the relations with my family were not good after that,” he continued. “My father is an angry man. He told me that he could not tolerate the fact that I call my son Donald Trump. So I left and moved my family to Kabul.”

The story of young Donald Trump, who is a year and a half old now, had largely remained private even after the family’s move to Kabul. But recently, a copy of the boy’s national ID started circulating on social media. Mr. Assadullah said it was put out by employees of the population registration department without his permission.

At the government office in Kabul responsible for verifying IDs from other provinces, Mr. Assadullah said he was treated with disrespect. He was even threatened with being sent to the Afghan intelligence agency for questioning, all for naming his son Donald Trump.

“When I went there, the employees of the department saw the name and they asked me, ‘What is this? Donald Trump?’ I said yes, is there any problem?” Mr. Assadullah said. “They looked at me funny, and they were saying, ‘Look, he named his son Donald Trump — what culture-less people.’ I told them their job is only to confirm the ID card.”

Critics say Mr. Assadullah named his son for the president to draw attention to himself and seek asylum abroad. But he rejected that idea, saying he never wanted his child’s identity to be so public.

Since news of young Donald Trump’s name spread, another family has come forward with a similar tale. Ghulam Ali Paiman, also from Shahristan in Daikundi, says he had twins nearly two years ago and named one child Vladimir Putin and the second Barack Hussein Obama. But there was a disagreement: His wife had wanted to name the second child Trump.

His story, however, was hard to verify.

Mr. Paiman sent The New York Times copies of what he said were hospital birth certificates, but they were issued this week, nearly two years after the birth of the twins. The hospital director confirmed issuing the recent birth certificates, but said he couldn’t find children with those names born two years ago.

Traditionally, most families name their children on the sixth day — long after they have left the hospital, if they were delivered in a hospital at all.

Independent verification of Mr. Paiman’s story could not be found.

“It is the first time I am hearing these twins named Trump and Putin,” said Shafaq Yaqoobi, the district governor of Shahristan. “I know the father. I have never heard from him or anyone else that he named his twins Trump and Putin.”

“But I have heard about Donald Trump,” he added, “whose father is Sayed Assadullah.”